# Let P(x)=2x^3-4x^2+2x-1. Evaluate P(x) by substituting the given value of x into the polynomial and simplifying. Then evaluate the polynomial by using the remainder theorem and synthetic division. P(-4)

Let $P\left(x\right)=2{x}^{3}-4{x}^{2}+2x-1$.
Evaluate P(x) by substituting the given value of x into the polynomial and simplifying. Then evaluate the polynomial by using the remainder theorem and synthetic division. P(-4)
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Karson French
$P\left(-4\right)=2{x}^{3}-4{x}^{2}+2x-1$ write the function
$=2\left(-4{\right)}^{3}-4\left(-4{\right)}^{2}+2\left(-4\right)-1$ substitute the values
=2(-64)-4(16)+2(-4)-1 evaluate the exponents
-128-64-8-1 perform multiplication
-201 remainder
Perform synthetic division to determine the remainder:
polyhorner scheme $\left[x=-4\right]\left\{2{x}^{3}-4{x}^{2}+2x-1\right\}$
Result:
P(-4)=-201